Heavy Industry

The goal of this post is to try to understand the role of money and debt in the economy. This is a complex story, but we will begin with some broad strokes.

Often discussions of money describe two “stages” in economic development. In the first stage, barter predominates. By the second stage, money is used as the medium of exchange. In between, there are various forms of specie competing for the role of money. However, present economic life is dominated by a third stage, namely money as the object of accumulation. To see the distinction, consider a simple example of an exchange economy.

The Exchange Economy

The farmer that brings his crops to market. The crops are exchanged for money. The farmer walks a few paces to the next stand and uses the proceeds to purchase consumption goods (a new copy of Adam Smith’s The Wealth of Nations) and capital goods (a new plow, or a deed to additional land). The farmer leaves the market carrying the new goods, but with no money profits. Profits are in the form of tangible goods, and wealth accumulation is primarily expressed as the accumulation of land.

Now, this of course is an ideal portrait. Before the 19th century, money accumulation did occur, primarily to fund military projects and a (proportionally small) trade in manufactures and luxury goods, but relative to the size of the economy, a negligible amount of profits were in the form of financial assets, as opposed to tangible assets. The wealthy of the world were so because of their command of land, and the ability to work the land.

In such an economy, the role of money can be ignored (what economists still trapped in the world of Adam Smith and Ricardo disparagingly term “nominal effects”). Money is simply a technical tool to facilitate transactions, and does not significantly alter the workings of the economy.

The Accumulation Economy

However, with the advent of the industrial era, and necessarily of banking, money itself grew in importance, becoming the primary object of accumulation. The presence of money accumulation introduces new instabilities in the system. In this model, transactions are motivated by profits. Businesses are required to spend less on wages and input goods than they receive from sales. Households are required to spend less on goods purchased from businesses than they receive from wages. The motivation is not to exchange goods, but to accumulate financial profits.

Imagine a system of nodes representing economic agents that are capable of incurring debt and earning a profit. The nodes represent households, businesses, and governments.

During a sample time, the nodes exchange cash with each other, spending and receiving money. The exchanges are done to facilitate the the market for goods, which is to say, the buying and selling goods and services, including labor.

At the end of the sample time, some nodes have accumulated a profit, and others a deficit. The key point is that we cannot all be cashflow positive. For one node to achieve a profit, there must be a corresponding deficit elsewhere in the network. The deficit spending, i.e. spending in excess of receipts, is achieved through borrowing. In practice, the deficit spending occurs through debts for purchase durable goods such as houses, cars, tuition, or government deficit spending. But, for the system to be maintained, ever greater amounts must be borrowed by succeeding generations in order to allow for the majority of nodes to be cash flow positive even as they are servicing the debt.

It is a requirement, that for Coca-Cola to achieve a profit — any profit — the public must be engaged in borrowing to buy a house or a car. Without deficit spending primarily by households and governments, there would be no possibility for businesses to be cash flow positive. There would be no opportunity for “thrifty” households to accumulate financial assets. Without an expansion in borrowing, all profits would be driven to zero, and the value of financial assets would be driven to zero as well. In such an environment, as soon as a single household attempted to spend less than they earn, that household would have its wages reduced, or costs increased, since there would be no balancing node willing to take on additional debt to fund the thrifty household’s profit.

So, in order for participants in the goods market to realize profits, those nodes which realize the profit must turn around and lend the proceeds to the deficit nodes, to fund the profit. So, there is a parallel market, the financial market, representing the buying and selling of claims on future cash flows from the goods market. Accumulated cash flow surpluses are channeled into the financial market, where the money is supplied to deficit nodes in exchange for interest payments.

The Flow Equation

Returning to our network of nodes, during the sample time, from a purely cash-flow analysis, we have the following equation:

D = total indebtedness
C = Aggregate positive cash flow in the goods market during the sample time.
I = interest payments on the existing debt stock made during the sample time.

Note that the sum of positive cash flows is defined as adding up all the surplus cash flows for those nodes which have positive cash flow — this amount is of course the same as the cash flow deficit for those nodes which are in the red. The integral of C(t) is a good approximation for total profits during a given period (it differs only when nodes switch between being cash flow positive and negative, so in theory the integral of C can be greater than profits during the same period. We will ignore this distinction.)

Also note that the interest rate, r(t), is not the offered rate, but the realized rate for the entire debt stock. Because of this, r(t) adjusts much more slowly than the market rate. It is the rigidity of r(t), together with the inability of prediction markets (i.e. the financial markets) to accurately predict cash flows which forces nominal effects to dominate debt deflation and inflation. Rather than “menu costs”, interest rate mismatch drives nominal effects.

At the next tick of the clock, in order to continue to produce output, additional profits need to be obtained, but now interest must be paid on the current debt stock.

So we have the debt flow equation, representing contributions from both markets. Assuming the unit of time is in years, we have:

where
C(t) = aggregate positive cash flow at time (t)
r(t) = (base-e) annual interest rate = logarithmic derivative of aggregate interest payments.
D(t) = total debt.

Evolution of the Debt to Output ratio

We are interested in ratios, specifically the debt to output ratio, in order to determine the sustainability of borrowing, and the potential mechanisms of reducing the debt to output ratio.

Setting:

a = ratio of debt to output
g = logarithmic derivative of output
r = continuous (base e) interest rate on existing debt stock
c = ratio of aggregate cash flow to economic output

we obtain the debt to output equation:

First Impressions

In order to obtain a bounded debt to output ratio without credit collapse, investors would need to anticipate cash flows and economic growth, and demand an appropriately matching interest rate. However, the mechanism for setting interest rates is determined by perceptions of risk and expected future cash flows. Specifically, low interest rates correspond to a low perception of risk and require high cash flows, whereas high interest rates correspond to an increased perception of risk and lower economic growth. Therefore individual profit maximization serves to drive up the ratio — no “irrationality” assumptions are necessary.

Second, the key to reducing the debt to output ratio is not to encourage households to “save” more, which would only increase the ratio, but rather to ensure that the difference between the realized interest rate and the output growth rate be negative. Fortunately, when the ratio is high, the term p(t) is negligible, and so rejoinders to be thrifty are ignorant but mostly harmless. The key is to either re-finance or default on a sufficient amount of debt to reduce the realized interest rate.

Third, it is clear from the equation that it is extremely difficult for the debt to output ratio to decrease when output is falling. Only when growth rates increase is there a real possibility of bringing the debt to output ratio down. Note that in the depression, the ratio almost doubled in the time period from 1930-33.

Fourth, government actions to purchase debt with printed money are an effective mechanism to “re-finance” debt, and are most effective when the purchased debt is of long enough duration that the interest rate remains low when growth resumes, and when the interest rate on the purchased assets is high relative to the interest rate of government debt.

Fifth, we see the impossibility of 100% reserve banking, because non-zero interest payments preclude the full funding of deficit nodes by surplus nodes. Banks (or other investement vehicles) must lend more to the deficit nodes than the surplus nodes can fund simply by accumulating positive cash flows in the goods economy. The financial market must expand above and beyond the profit needs of the goods markets.